It is known that blends of linear low polyethylene (LLDPE) and polypropylene (PP) have improved stiffness (higher modulus) than LLDPE alone. Such blends exhibit a catastrophic decrease in impact and in tear strength, particularly in the machine direction (MD). We have found that LLDPE/PP blends containing minor amounts of an ethylene-propylene rubber (EPR) have the expected increase in stiffness along with unexpectedly improved MD Elmendorf tear and dart drop impact properties.